Generation of inclined protoplanetary discs and misaligned planets through mass accretion I: Coplanar secondary discs

We study the three-dimensional evolution of a viscous protoplanetary disc which accretes gas material from a second protoplanetary disc during a close encounter in an embedded star cluster. The aim is to investigate the capability of the mass accretion scenario to generate strongly inclined gaseous discs which could later form misaligned planets. We use smoothed particle hydrodynamics to study mass transfer and disc inclination for passing stars and circumstellar discs with different masses. We explore different orbital configurations to find the parameter space which allows significant disc inclination generation. \citet{Thi2011} suggested that significant disc inclination and disc or planetary system shrinkage can generally be produced by the accretion of external gas material with a different angular momentum. We found that this condition can be fullfilled for a large range of gas mass and angular momentum. For all encounters, mass accretion from the secondary disc increases with decreasing mass of the secondary proto-star. Thus, higher disc inclinations can be attained for lower secondary stellar masses. Variations of the secondary disc's orientation relative to the orbital plane can alter the disc evolution significantly. The results taken together show that mass accretion can change the three-dimensional disc orientation significantly resulting in strongly inclined discs. In combination with the gravitational interaction between the two star-disc systems, this scenario is relevant for explaining the formation of highly inclined discs which could later form misaligned planets.Comment: 13 pages, accepted for publication in MNRA

Evolution of a disc-planet system with a binary companion on an inclined orbit

We study orbital inclination changes associated with the precession of a disc-planet system that occurs through gravitational interaction with a binary companion on an inclined orbit. We investigate whether this scenario can account for giant planets on close orbits highly inclined to the stellar equatorial plane. We obtain conditions for maintaining approximate coplanarity and test them with SPH-simulations. For parameters of interest, the system undergoes approximate rigid body precession with modest warping while the planets migrate inwards. Because of pressure forces, disc self-gravity is not needed to maintain the configuration. We consider a disc and single planet for different initial inclinations of the binary orbit to the midplane of the combined system and a system of three planets for which migration leads to dynamical instability that reorders the planets. As the interaction is dominated by the time averaged quadrupole component of the binary's perturbing potential, results for a circular orbit can be scaled to apply to eccentric orbits. The system responded adiabatically when changes to binary orbital parameters occurred on time scales exceeding the orbital period. Accordingly inclination changes are maintained under its slow removal. Thus the scenario for generating high inclination planetary orbits studied here, is promising.Comment: 16 pages, 13 figures, accepted for publication by MNRA

Bayesian Posterior Contraction Rates for Linear Severely Ill-posed Inverse Problems

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function. If the observational noise is assumed to be Gaussian then this prior is conjugate to the likelihood so that the posterior distribution is also Gaussian. We study Bayesian posterior consistency in the small observational noise limit. We assume that the forward operator and the prior and noise covariance operators commute with one another. We show how, for given smoothness assumptions on the truth, the scale parameter of the prior can be adjusted to optimize the rate of posterior contraction to the truth, and we explicitly compute the logarithmic rate.Comment: 25 pages, 2 figure

Disorder effect in low dimensional superconductors

The quasiparticle density of states (DOS), the energy gap, the superfluid density $\rho_s$, and the localization effect in the s- and d-wave superconductors with non-magnetic impurity in two dimensions (2D) are studied numerically. For strong (unitary) scatters, we find that it is the range of the scattering potential rather than the symmetry of the superconducting pairing which is more important in explaining the impurity dependences of the specific heat and the superconducting transition temperature in Zn doped YBCO. The localization length is longer in the d-wave superconducting state than in the normal state, even in the vicinity of the Fermi energy.Comment: 2 pages, uuencoded compressed postscript file, IRC-940610

Optimizing Hartree-Fock orbitals by the density-matrix renormalization group

We have proposed a density-matrix renormalization group (DMRG) scheme to optimize the one-electron basis states of molecules. It improves significantly the accuracy and efficiency of the DMRG in the study of quantum chemistry or other many-fermion system with nonlocal interactions. For a water molecule, we find that the ground state energy obtained by the DMRG with only 61 optimized orbitals already reaches the accuracy of best quantum Monte Carlo calculation with 92 orbitals.Comment: published version, 4 pages, 4 figure

Three-Dimensional MHD Simulation of Caltech Plasma Jet Experiment: First Results

Magnetic fields are believed to play an essential role in astrophysical jets with observations suggesting the presence of helical magnetic fields. Here, we present three-dimensional (3D) ideal MHD simulationsof the Caltech plasma jet experiment using a magnetic tower scenario as the baseline model. Magnetic fields consist of an initially localized dipole-like poloidal component and a toroidal component that is continuously being injected into the domain. This flux injection mimics the poloidal currents driven by the anode-cathode voltage drop in the experiment. The injected toroidal field stretches the poloidal fields to large distances, while forming a collimated jet along with several other key features. Detailed comparisons between 3D MHD simulations and experimental measurements provide a comprehensive description of the interplay among magnetic force, pressure and flow effects. In particular, we delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms. With suitably chosen parameters that are derived from experiments, the jet in the simulation agrees quantitatively with the experimental jet in terms of magnetic/kinetic/inertial energy, total poloidal current, voltage, jet radius, and jet propagation velocity. Specifically, the jet velocity in the simulation is proportional to the poloidal current divided by the square root of the jet density, in agreement with both the experiment and analytical theory. This work provides a new and quantitative method for relating experiments, numerical simulations and astrophysical observation, and demonstrates the possibility of using terrestrial laboratory experiments to study astrophysical jets.Comment: accepted by ApJ 37 pages, 15 figures, 2 table